Vjylku

I recently had my second lecture in Thermodynamics, a long lecture which involved the first law and a portion of the second law, at some point during the lecture we defined entropy as the change of heat energy per unit temperature, and from this we derived a general expression for entropy (using laws derived for ideal gases) in which it was clear that it depended on the change of temperature and volume through the process as well as the number of moles.

I have also learned that Entropy is a measure of disorder in a system which was non sense to me especially that I don't understand how disorder(chaotic movement of particles) is related to the change in heat energy per unit temperature, its more related to specific heat if you ask me, nonetheless In attempts to understand what's useful in knowing whats the amount of disorder in a system I learnt that it measures the state of reversibility of the process which still doesn't make sense when trying to relate it with the '' change in heat energy per unit temperature ''.

TL;DR
I need an answer these questions:

1. A process has an entropy of X what does this tell me, another process has higher entropy what does this tell me, how can I relate the definition of entropy to '' change in heat energy per unit time''.

Please don't explain using statistical thermodynamics.

This is a big topic with many aspects but let me start with the reason why entropy and the second law was needed.

You know the first law is conservation of energy. If a hot body is placed in contact with a cold body heat normally flows from the hot body to the cold . Energy lost by the hot body equals energy gained by the cold body. Energy is conserved and the first law obeyed.

But that law would also be satisfied if the same amount of heat flowed in the other direction. However one never sees that happen naturally (without doing work). What is more after transferring heat from hot to cold you would not expect it to spontaneously reverse itself. The process is irreversible.

The second law and the property of entropy was developed to show how that cannot happen.

ADDENDUM:

Found a little more time to bring this to the next level. This will tie in what I said above to the actual second law and the property of entropy.

So we needed a new law and property that would be violated if heat flowed naturally from a cold body to a hot body. The property is called entropy, $S$, which obeys the following inequality:

$$Delta S_{tot}=Delta S_{sys}+Delta S_{surr}≥0$$

Where $Delta S_{tot}$ is the total entropy change of the system plus the surrounding (entropy change of the universe) for any process where the system and surroundings interact. The equality applies if the process is reversible, and the inequality if it is irreversible. Since all real processes are irreversible (explained below), the law tells us that the total entropy of the universe increases as a result of a real process.

The property of entropy is defined as

$$dS=frac {dQ_{rev}}{T}$$

where $dQ$ is a reversible differential transfer of heat and $T$ is the temperature at which it is transferred. Although it I defined for a reversible transfer of heat, it applies to any process between two states. If the process occurs at constant temperature, we can say

$$Delta S=frac{Q}{T}$$

where Q is the heat transferred to the system at constant temperature.

We apply this new law to our hot and cold bodies and call them bodies A and B. To make things simple, we stipulate that the bodies are massive enough (or the amount of heat Q transferred small enough) that their temperatures stay constant during the heat transfer Applying the second law to our bodies:

$$Delta S_{tot}=frac{-Q}{T_A}+frac{+Q}{T_B}$$

The minus sign for body A simply means the entropy decrease for that body because heat is transferred out, and the positive sign for body B means its entropy has increased because heat is transferred in.

From the equation, we observe that for all $T_{A}>T_{B}$, $Delta S_{tot}>0$. We further note that as the two temperatures get closer and closer to each other, $Delta S_{tot}$ goes to 0. But if $T_{A}<T_{B}$ meaning heat transfers from the cold body to the hot body, $Delta S$ would be less than zero, violating the second law. Thus the second law precludes that natural transfer of heat from a cold body to a hot body.

Note that for $Delta S_{tot}=0$ the temperatures would have to be equal. But we know that heat will not flow unless there is a temperature difference. So we see that for all real heat transfer processes, such processes are irreversible.

Irreversibility and entropy increase is not limited to heat transfer processes. Any process goes from a state of disequilibrium to equilibrium. Beside heat, you have processes involving pressure differentials (pressure disequilibrium). These process are also irreversible and generate entropy.

Hope this helps.

Entropy is overloaded term. However, in thermodynamics, it has simple meanings.

First, entropy of system is a quantity that depends only on the equilibrium state of that system. This is by definition; entropy is defined for a state. If the system is not in equilibrium state, it may or may not have an entropy. But if it is in equilibrium state, it does have entropy.

The value of entropy for some state that we study does not tell us much. This value is rarely of practical interest.

The reason we talk about entropy is often because it has interesting behaviour: if reversible process happens inside a closed thermally isolated system, entropy of the closed system remains constant, while if non-reversible process happens, its value increases (by how much cannot be universally stated, it may be negligible or huge, but it definitely cannot decrease). This is another way to state the 2nd law of thermodynamics.

If you want to understand how this entropy is connected to things like order or information on the molecular level, you have to study statistical physics of molecules. In thermodynamics proper, there is nothing that would connect entropy to such things.